\(\renewcommand{\hat}[1]{\widehat{#1}}\)

Shared Qs (025)


  1. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

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    Plot 2

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    Plot 3

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    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  2. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

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    Plot 2

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    Plot 3

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    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  3. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

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    Plot 2

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    Plot 3

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    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  4. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

    plot of chunk unnamed-chunk-2

    Plot 2

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    Plot 3

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    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  5. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

    plot of chunk unnamed-chunk-2

    Plot 2

    plot of chunk unnamed-chunk-2

    Plot 3

    plot of chunk unnamed-chunk-2

    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  6. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

    plot of chunk unnamed-chunk-2

    Plot 2

    plot of chunk unnamed-chunk-2

    Plot 3

    plot of chunk unnamed-chunk-2

    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  7. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

    plot of chunk unnamed-chunk-2

    Plot 2

    plot of chunk unnamed-chunk-2

    Plot 3

    plot of chunk unnamed-chunk-2

    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  8. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

    plot of chunk unnamed-chunk-2

    Plot 2

    plot of chunk unnamed-chunk-2

    Plot 3

    plot of chunk unnamed-chunk-2

    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  9. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

    plot of chunk unnamed-chunk-2

    Plot 2

    plot of chunk unnamed-chunk-2

    Plot 3

    plot of chunk unnamed-chunk-2

    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  10. Question

    Match each plot with its function. Different sources define arccot with different ranges. I’ve followed the arccot defined by Desmos and wikipedia, with a range of \(\left[0,\pi\right]\), not \(\left[\frac{-\pi}{2},\,\frac{\pi}{2}\right]\). This choice gives a continuous function, but means that when \(m<0\), \(\arctan(\frac{1}{m})\ne \mathrm{arccot}(m)\). The other possible definition (not used here) is seen on Wolfram Alpha.

    Plot 1

    plot of chunk unnamed-chunk-2

    Plot 2

    plot of chunk unnamed-chunk-2

    Plot 3

    plot of chunk unnamed-chunk-2

    Plot 4

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    Plot 5

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    Plot 6

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    Plot 7

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    Plot 8

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    Plot 9

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    Plot 10

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    Plot 11

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    Plot 12

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    Solution


  11. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  12. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  13. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  14. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  15. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  16. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  17. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  18. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  19. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  20. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the amplitude of the sinusoidal function graphed above.


    Solution


  21. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  22. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  23. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  24. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  25. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  26. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  27. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  28. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  29. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  30. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the period of the sinusoidal function graphed above.


    Solution


  31. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  32. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  33. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  34. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  35. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  36. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  37. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  38. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  39. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  40. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the vertical shift of the sinusoidal function graphed above.


    Solution


  41. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  42. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  43. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  44. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  45. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  46. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  47. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  48. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  49. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  50. Question

    Some quantity (\(y\)) is varying in time (\(t\)), following a temporal sinusoidal function parameterized with 4 parameters:

    \[y(t) ~=~ A\sin\left(\frac{2\pi}{P}(t+L)\right)+D\]

    Those four parameters were randomly assigned values, producing the graph below.

    plot of chunk unnamed-chunk-2

    Estimate the leftward (back in time) shift of the sinusoidal function graphed above.


    Solution


  51. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((0.06, 1.17)\) and the first minimum is \((0.28, 0.29)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  52. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((2.42, 1.54)\) and the first minimum is \((1.16, -1.06)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  53. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((1.39, 1.01)\) and the first minimum is \((0.45, -1.61)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  54. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((0.98, 1.09)\) and the first minimum is \((0.46, 0.41)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  55. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((2.64, 1.24)\) and the first minimum is \((1.16, 0.18)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  56. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((0.01, 0.57)\) and the first minimum is \((0.19, -1.79)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  57. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((0.46, 0.5)\) and the first minimum is \((0.22, -0.94)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  58. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((0.22, 2.11)\) and the first minimum is \((0.02, -2.65)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  59. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((1.75, 1.33)\) and the first minimum is \((0.53, 0.27)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution


  60. Question

    To generate the plot below, four parameters (\(A\), \(B\), \(C\), and \(D\)) where randomly selected and plugged into the following sinusoidal function:

    \[y(t) = A\sin(Bt+C)+D\]

    where \[A>0\] and \[0\le C < 2 \pi\]

    plot of chunk unnamed-chunk-2

    The first maximum is \((0.33, 0.79)\) and the first minimum is \((0.81, -1.91)\). Determine the values of the parameters (rounded to the nearest hundredth).



    Solution